I am shocked at the inconsistencies. I'm not trying to propagate any conspiracy theories, but there is a big difference between what was initially reported, to what president Obama said, to what was reported later, and later spoken by officials. Seems like the story keeps changing. I'm not sure who's to blame, but it's a little disconcerting.
Looking at some of the things that you're talking about here makes me think that you were dealing with some really low reliability sources. From where I am, the official sources have been surprisingly consistent.
I first heard a bomb killed him.
Then he was shot by Navy SEALs.
Wow. A bomb? Where did you hear that? I only ever heard he was shot. Of course, there were all sorts of journalists making up crap because "it sounds reasonable until we get actual confirmation". Many people were taking guesses because they thought (and probably still do) that its better to have complete information than completely correct information.
He was using a human shield
He was pointed out by a wife
He wasn't using a human shield
His wife was running away.
All I have heard (from official sources): Human shields were used. He was found with one of his wives. His wife was wounded but not killed in the encounter. I'm seriously dubious of the rest.
As far as the "double tap" goes, that implies something semi-automatic and not fully automatic. Submachine guns have a very high rate of fire and you are likely to get more than 2 shots for every trigger squeeze. It's definately possible to get only 2 with a quick trigger pull however.
Special forces --and in particular counter-terrorist teams-- (in the US, at least) generally never use the full-auto setting on their sub-machine guns. They will use either the 3-round or 1-round settings. There were multiple sources (both executive and military) that declared the team was sent in with orders to keep non-combatant casualties to an absolute minimum. Though I know it breaks the hearts of thousands of 12 year-old CoD fans out there, you just don't use the full-auto setting on sub-machine guns in that sort of setting.
The muzzle rise may explain this, or they could have done a quick "two to the chest, one to the head" as is commonly trained. It could have also been multiple shooters (you see this happen a lot in police officer shootings).
It was already confirmed that there were only two shots. It was also confirmed that it was a single shooter. And then we've got the founder of SEAL Team Six saying that they are trained to use two-shot bursts in this sort of situation. And that's not just a SEAL thing. I believe it was some SAS guys who first started training that way.